Heat oil in large pot on medium. Add kielbasa and cook, stirring occasionally, until browned, 4 to 5 minutes. Using slotted spoon, transfer sausage to plate.
Add garlic to pot and cook, stirring, 1 minute (do not let it brown). Add wine and simmer, scraping up any browned bits, 1 minute.
Add broth and pasta and bring to a boil. Reduce heat and simmer until pasta is just tender, 8 to 10 minutes.
Add beans, sausage, and ½ teaspoon pepper and cook until heated through, about 2 minutes. Remove from heat and add spinach, stirring gently until it begins to wilt. Serve with Parmesan.
